A flurry of recent articles has argued on the basis of constructed European wide monetary aggregates that the demand for EURO's will be more stable than the current demand for national currencies. In policy circles this seemingly moderating effect of monetary integration figures as an additional argument pro union. On the basis of the standard foreign exchange rate model we argue that once the uncoordinated country specific money supply system is abolished, the coherence between local monetary aggregates increases dramatically, leaving little room for a free ride on the law of large numbers. The only road towards stability is prudent monetary policy.